1. Field of the Invention
The present invention relates to a drop shock analysis system using an FEM (Finite Element Method) and more particularly to an analysis method using the FEM for analyzing a drop shock of an electronic device, a program for the analysis by the FEM method, and an FEM analysis system.
The present application claims priority of Japanese Patent Application No. 2001-164730 filed on May 31, 2001, which is hereby incorporated by reference.
2. Description of the Related Art
Since it is expected that, by using a stress analysis (by way of simulation) based on an FEM, a number of times of manufacturing a prototype and of experiments can be reduced and a development period can be shortened, the stress analysis using the FEM is now being carried out increasingly in businesses or universities.
The stress analysis can be classified into two types, one being a static analysis and another being a dynamic analysis. A method for the stress analysis can also be classified into two types, one being an implicit method and another being an explicit method. These two methods are different from each other in that an expression of the implicit method contains a spring constant “k” as a matrix, thereby forming a non-diagonal matrix and an expression of the explicit method contains a mass “m” as a matrix, thereby forming a diagonal matrix. Therefore, when the stress analysis is performed, an inverse matrix calculation of the spring constant “k” takes more time than an inverse matrix calculation of the mass “m”. Moreover, in the case of the implicit method, a simultaneous linear equation is solved so that an equilibrium condition is satisfied and therefore accuracy of a stress analysis is higher compared with the explicit method, however, more time is required for the analysis compared with the explicit method.
Each of the implicit and explicit methods has an advantage and a disadvantage. As a result, the implicit method is used for the static analysis not requiring so much time and the explicit method is used, in most cases, for the dynamic analysis requiring much time. Under present circumstances, in an automobile industry having a most advanced drop shock (crash) analysis technology being a field of the present invention, in particular, the stress analysis is performed by using an explicit method-specific software typified by PAM-SHOCK and LS-DYNA. FIG. 4 is a flowchart showing one example of the analysis processing operation in a conventional FEM analysis system. That is, in Step A301, whether or not an analysis to be made is a shock analysis is judged and, if it is the shock analysis, the explicit method provided in Step A303 is used unconditionally and, if it is not the shock analysis, a subsequent process is relegated to a judgement of the analyzer in Step A304.
In such circumstances, sizes and weights of electronic devices are being reduced rapidly in recent years and a cellular phone or a like becomes widespread remarkably in particular, however, a problem occurs in that, when it is dropped while carrying it, a connected portion of an LSI chip embedded therein is broken. In order to evaluate connection reliability of portable electronic devices, an actual drop test is required using actual electronic devices, however, the experiment entails high costs and time. Therefore, a demand for reduction in costs required in such experiments for a drop shock analysis is increasing. In an attempt to respond to this demand, a method using a shock analysis technique cultivated through experiences in automobiles was tried by some universities, however, values calculated in experiments are not in agreement with actual phenomena, for example, reaction force (impact force) is extraordinarily larger (that is, larger by one to two digits) than calculated values and it is therefore expected that a new method of an analysis of a drop shock that can be used for the analysis of electronic devices is developed.
A reason why behavior (deformation of each part) and reaction force (impact force) are widely different from actual phenomena when the explicit method is used for a dynamic analysis, in particular, for a drop analysis of portable electronic devices is explained below.
When “Δtex” is defined to be an analysis time interval in the explicit method and “Δtim” is defined to be an analysis time interval in the implicit method, a constraint in the implicit method is only a converging calculation of displacement obtained from an equilibrium equation in every step while the dynamic analysis is performed in the explicit method and therefore there is a following constraint (Courant condition) related to a minimum mesh size, longitudinal elastic modulus, and mass density:Δtex<L/c  Expression (3)c=(E/ρ)1/2  Expression (4)where “L” denotes a minimum mesh size in an analysis model, “c” denotes a propagation speed of an elastic wave, “E” denotes a longitudinal elastic modulus (also being called “Young's modulus”) and “ρ” denotes mass density. Thus, since the explicit method has a property that it depends on the analysis time interval Δtex and since the analysis time interval Δtex has a constraint by a minimum mesh size “L” as shown in the expression (3), the analysis time interval Δtex becomes too small in the analysis model for a small-sized portable electronic device. Therefore, a following expression (5) is given:α≈v/Δtex,F=mα  Expression (5)where “α” denotes acceleration, “m” denotes a mass, “F” denotes reaction force, and “v” denotes a drop velocity. As a result, the calculation produces extremely large reaction force (impact force) F and different deformation occurs.
As one example, when a body is dropped from a height of 1000 mm, due to a law of conservation of energy, a following equation (6) is given:v=(2gh)1/2=4400 mm/s  Expression (6)where “g” denotes gravimetric acceleration and “h” denotes a dropped height. Since a phenomenon of about 5×10−4 seconds is a problem in a drop of electronic devices, the acceleration “α” and the reaction force “F” have following values.α=4400×10000/5=8×106 mm/s2 F=0.1×8.8×106=880NAs a convergence stabilizing condition in the explicit method, the analysis time interval Δtex has to satisfy a following relation:Δtex<L/c andc=(E/ρ)1/2 
If a solder ball diameter is 1.0 mm, a Young's modulus E=19600 N/mm2, a density “ρ”=2×10−9 kg/mm3, c=3.2×106 m/s. Here, if the solder ball diameter is divided into four portions, L/c=0.25/(3.2×106) seconds=7.8×10−8 seconds.
Therefore, in order to analyze a drop phenomenon at a speed of 5×10−4 seconds, in the implicit method, by reducing the acceleration “α” to one tenth (that is, a digit is reduced by one), its analysis is made possible, while, in the case of the explicit method, an analysis time interval has to be reduced to one thousands.
As described above, if an analysis time interval is same, since a number of times of the analysis required to reach the value of 5×10−4 seconds becomes same, time required for a total analysis becomes more shorter in the explicit method in which time required for one time analysis becomes short because of use of an expression of a diagonal matrix compared with the implicit method.
However, if the analysis time interval required for satisfying conditions for stabilization in the explicit method becomes extraordinarily smaller compared with that in the implicit method because a fine mesh is contained like in the case of a model for portable electronic devices, a number of times of the explicit method=(analysis time interval in the implicit method/analysis time interval in the explicit method)×(number of times in the implicit method). As a result, due to an increased number of the analysis in the explicit method, time required for the total analysis is increased more in the explicit method compared with the implicit method.
Moreover, in the analysis during the very short time interval, there are some cases in which shock force increases and deformation state is not in agreement with an actual phenomenon. In the above example, in the case of the implicit method, a value approaching to a result from a calculation on paper can be acquired by using a shock force of about 980N, however, in the case of the explicit method, about one hundred-folded shock force is necessary.